The phase diagram of magnetic ladders constructed from a composite-spin model

White's density matrix renormalization group ({DMRG}) method has been applied to an $S= 1/2 + 1/2$ composite-spin model, which can also be considered as a two-leg ladder model. By appropriate choices of the coupling constants this model allows not only to study how the gap is opened around the gapless integrable models, but also to interpolate continuously between models with different spin lengths. We have found indications for the existence of several different massive phases.